Mini-Workshop: Entropy, Information and Control

This mini-workshop was motivated by the emerging field of networked control, which combines concepts from the disciplines of control theory, information theory and dynamical systems. Many current approaches to networked control simplify one or more of these three aspects, for instance by assuming no dynamical disturbances, or noiseless communication channels, or linear dynamics. The aim of this meeting was to approach a common understanding of the relevant results and techniques from each discipline in order to study the major, multi-disciplinary problems in networked control

Exploiting timing information in event-triggered stabilization of linear systems with disturbances

In the same way that subsequent pauses in spoken language are used to convey information, it is also possible to transmit information in communication networks not only by message content, but also with its timing. This paper presents an event-triggering strategy that utilizes timing information by transmitting in a state-dependent fashion. We consider the stabilization of a continuous-time, time-invariant, linear plant over a digital communication channel with bounded delay and subject to bounded plant disturbances and establish two main results. On the one hand, we design an encoding-decoding scheme that guarantees a sufficient information transmission rate for stabilization. On the other hand, we determine a lower bound on the information transmission rate necessary for stabilization by any control policy

Information theoretic aspects of the control and the mode estimation of stochastic systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (leaves 131-137).(cont.) parallel with a communication paradigm and deriving an analysis of performance. In our approach, the switching system is viewed as an encoder of the mode, which is interpreted as the message, while a probing signal establishes a random code. Using a distortion function, we define an uncertainty ball where the estimates are guaranteed to lie with probability arbitrarily close to 1. The radius of the uncertainty ball is directly related to the entropy rate of the switching process.In this thesis, we investigate three problems: the first broaches the control under information constraints in the presence of uncertainty; in the second we derive a new fundamental limitation of performance in the presence of finite capacity feedback; while the third studies the estimation of Hidden Markov Models. Problem 1: We study the stabilizability of uncertain stochastic systems in the presence of finite capacity feedback. We consider a stochastic digital link that sends words whose size is governed by a random process. Such link is used to transmit state measurements between the plant and the controller. We derive necessary and sufficient conditions for internal and external stabilizability of the feedback loop. In addition, stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. Problem 2: We address a fundamental limitation of performance for feedback systems, in the presence of a communication channel. The feedback loop comprises a discrete-time, linear and time-invariant plant, a channel, an encoder and a decoder which may also embody a controller. We derive an inequality of the form L ̲>[or equal to] [epsilon]max ... - C[channel] where L ̲is a measure of disturbance rejection, A is the open loop dynamic matrix and Cchannel is the Shannon capacity of the channel. Our measure L ̲is non-negative and smaller L ̲indicates better rejection (attenuation), while L ̲= 0 signifies no rejection. Additionally, we prove that, under a stationarity assumption, L ̲admits a log-sensitivity integral representation. Problem 3: We tackle the problem of mode estimation in switching systems. From the theoretical point of view, our contribution is twofold: creating a framework that has a clearby Numo Miguel Lara Cintra Martins.Ph.D